Bayesian Structural Learning with Parametric Marginals for Count Data: An Application to Microbiota Systems

High dimensional and heterogeneous count data are collected in various applied fields. In this paper, we look closely at high-resolution sequencing data on the microbiome, which have enabled researchers to study the genomes of entire microbial communities. Revealing the underlying interactions between these communities is of vital importance to learn how microbes influence human health. To perform structural learning from multivariate count data such as these, we develop a novel Gaussian copula graphical model with two key elements. Firstly, we employ parametric regression to characterize the marginal distributions. This step is crucial for accommodating the impact of external covariates. Neglecting this adjustment could potentially introduce distortions in the inference of the underlying network of dependences. Secondly, we advance a Bayesian structure learning framework, based on a computationally efficient search algorithm that is suited to high dimensionality. The approach returns simultaneous inference of the marginal effects and of the dependence structure, including graph uncertainty estimates. A simulation study and a real data analysis of microbiome data highlight the applicability of the proposed approach at inferring networks from multivariate count data in general, and its relevance to microbiome analyses in particular. The proposed method is implemented in the R package BDgraph

Utilizing gene co-expression networks for comparative transcriptomic analyses

The development of high-throughput technologies such as microarray and next-generation RNA sequencing (RNA-seq) has generated numerous transcriptomic data that can be used for comparative transcriptomics studies. Transcriptomes obtained from different species can reveal differentially expressed genes that underlie species-specific traits. It also has the potential to identify genes that have conserved gene expression patterns. However, differential expression alone does not provide information about how the genes relate to each other in terms of gene expression or if groups of genes are correlated in similar ways across species, tissues, etc. This makes gene expression networks, such as co-expression networks, valuable in terms of finding similarities or differences between genes based on their relationships with other genes. The desired outcome of this research was to develop methods for comparative transcriptomics, specifically for comparing gene co-expression networks (GCNs), either within or between any set of organisms. These networks represent genes as nodes in the network, and pairs of genes may be connected by an edge representing the strength of the relationship between the pairs. We begin with a review of currently utilized techniques available that can be used or adapted to compare gene co-expression networks. We also work to systematically determine the appropriate number of samples needed to construct reproducible gene co-expression networks for comparison purposes. In order to systematically compare these replicate networks, software to visualize the relationship between replicate networks was created to determine when the consistency of the networks begins to plateau and if this is affected by factors such as tissue type and sample size. Finally, we developed a tool called Juxtapose that utilizes gene embedding to functionally interpret the commonalities and differences between a given set of co-expression networks constructed using transcriptome datasets from various organisms. A set of transcriptome datasets were utilized from publicly available sources as well as from collaborators. GTEx and Gene Expression Omnibus (GEO) RNA-seq datasets were used for the evaluation of the techniques proposed in this research. Skeletal cell datasets of closely related species and more evolutionarily distant organisms were also analyzed to investigate the evolutionary relationships of several skeletal cell types. We found evidence that data characteristics such as tissue origin, as well as the method used to construct gene co-expression networks, can substantially impact the number of samples required to generate reproducible networks. In particular, if a threshold is used to construct a gene co-expression network for downstream analyses, the number of samples used to construct the networks is an important consideration as many samples may be required to generate networks that have a reproducible edge order when sorted by edge weight. We also demonstrated the capabilities of our proposed method for comparing GCNs, Juxtapose, showing that it is capable of consistently matching up genes in identical networks, and it also reflects the similarity between different networks using cosine distance as a measure of gene similarity. Finally, we applied our proposed method to skeletal cell networks and find evidence of conserved gene relationships within skeletal GCNs from the same species and identify modules of genes with similar embeddings across species that are enriched for biological processes involved in cartilage and osteoblast development. Furthermore, smaller sub-networks of genes reflect the phylogenetic relationships of the species analyzed using our gene embedding strategy to compare the GCNs. This research has produced methodologies and tools that can be used for evolutionary studies and generalizable to scenarios other than cross-species comparisons, including co-expression network comparisons across tissues or conditions within the same species

Consistency of biological networks inferred from microarray and sequencing data

Background: Sparse Gaussian graphical models are popular for inferring biological networks, such as gene regulatory networks. In this paper, we investigate the consistency of these models across different data platforms, such as microarray and next generation sequencing, on the basis of a rich dataset containing samples that are profiled under both techniques as well as a large set of independent samples. Results: Our analysis shows that individual node variances can have a remarkable effect on the connectivity of the resulting network. Their inconsistency across platforms and the fact that the variability level of a node may not be linked to its regulatory role mean that, failing to scale the data prior to the network analysis, leads to networks that are not reproducible across different platforms and that may be misleading. Moreover, we show how the reproducibility of networks across different platforms is significantly higher if networks are summarised in terms of enrichment amongst functional groups of interest, such as pathways, rather than at the level of individual edges. Conclusions: Careful pre-processing of transcriptional data and summaries of networks beyond individual edges can improve the consistency of network inference across platforms. However, caution is needed at this stage in the (over)interpretation of gene regulatory networks inferred from biological data

Additional file 1 of Consistency of biological networks inferred from microarray and sequencing data

Simulation showing the effect of confounders on network reconstruction. (PDF 117 kb